Group #22609425 — subgroups

Subgroups — #22609425

Order 9344.

152 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 152 conjugacy classes of subgroups — too many to draw. Only its 57 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17988967	C₂	1	1	yes	maximal, characteristic
2	#17988872	C₂	1	2	yes	maximal
3	#17988338	C₂	1	1	yes	maximal, characteristic
4	#17988334	C₂	1	2	yes	maximal
5	#446×C₇₃	C₂	1	1	yes	maximal, characteristic
6	C₂×Dic₂₉₂	—	2	1	no	—
7	C₂×Dic₂₉₂	—	2	1	no	—
8	#14556591	C₂²	1	2	yes	—
9	#14556522	—	2	2	no	—
10	C₄⋊#10596831	C₂²	1	2	yes	—
11	#14556515	—	2	2	no	—
12	C₄×Q₈×C₇₃	C₂²	1	1	yes	characteristic
13	C₄⋊C₈×C₇₃	—	2	1	no	—
14	C₄⋊C₈×C₇₃	C₂²	1	1	yes	characteristic
15	#97×C₇₃	—	2	1	no	—
16	C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic
17	C₂×Dic₁₄₆	—	2	2	no	—
18	Dic₂₉₂	—	4	2	no	—
19	Dic₂₉₂	—	4	2	no	—
20	C₂×#10596831	—	2	2	no	—
21	C₄⋊Dic₇₃	—	2	2	no	—
22	C₄⋊Dic₇₃	—	2	2	no	—
23	C₂×Q₈×C₇₃	D₄	1	1	yes	characteristic
24	C₂×C₈×C₇₃	—	2	1	no	—
25	C₂×C₈×C₇₃	D₄	1	1	yes	characteristic
26	C₂×C₈×C₇₃	D₄	1	1	yes	characteristic
27	C₄⋊C₄×C₇₃	—	2	1	no	—
28	C₄⋊C₄×C₇₃	D₄	1	1	yes	characteristic
29	C₄²×C₇₃	—	2	1	no	—
30	C₄²×C₇₃	C₂³	1	1	yes	characteristic
31	Q₈×C₇₃	—	2	2	no	—
32	C₂×C₄×C₇₃	—	2	1	no	—
33	C₂×C₄×C₇₃	—	2	1	no	—
34	C₂×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
35	C₂×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
36	C₂×C₄×C₇₃	#41	1	1	yes	characteristic
37	C₂×Dic₇₃	—	4	2	no	—
38	Dic₁₄₆	—	4	2	no	—
39	Dic₁₄₆	—	4	2	no	—
40	C₈×C₇₃	—	2	1	no	—
41	C₈×C₇₃	—	4	1	no	—
42	C₈×C₇₃	SD₁₆	1	2	yes	—
43	#10596831	—	4	2	no	—
44	C₂²×C₇₃	#121	1	1	yes	characteristic
45	C₄×C₇₃	—	2	1	no	—
46	C₄×C₇₃	—	4	1	no	—
47	C₄×C₇₃	—	4	1	no	—
48	C₄×C₇₃	C₂×SD₁₆	1	1	yes	characteristic
49	C₄×C₇₃	AGL(1,ℤ/8)	1	1	yes	characteristic
50	C₄×C₇₃	#137	1	2	yes	—
51	Dic₇₃	—	8	2	no	—
52	C₂×C₇₃	#460	1	1	yes	characteristic
53	C₂×C₇₃	#470	1	1	yes	characteristic
54	C₂×C₇₃	#473	1	1	yes	characteristic
55	#1690	—	73	1	no	maximal, Sylow
56	C₇₃	#1690	1	1	yes	characteristic, complemented, Sylow
57	#494	—	73	1	no	—
58	#475	—	73	2	no	—
59	#446	D₇₃	1	1	yes	characteristic
60	#334	—	73	1	no	—
61	#332	—	73	2	no	—
62	C₂×Q₁₆	—	146	1	no	—
63	C₂×Q₁₆	—	146	1	no	—
64	C₄⋊Q₈	—	73	2	no	—
65	C₄×Q₈	C₂×D₇₃	1	1	yes	characteristic
66	#106	—	146	2	no	—
67	C₄⋊C₈	—	2	1	no	—
68	C₄⋊C₈	—	73	2	no	—
69	C₄⋊C₈	C₂×D₇₃	1	1	yes	characteristic
70	#103	—	146	2	no	—
71	#97	—	2	1	no	—
72	C₄×C₈	C₂×D₇₃	1	1	yes	characteristic
73	C₂×Q₈	—	146	2	no	—
74	C₂×Q₈	D₂₉₂	1	1	yes	characteristic
75	Q₁₆	—	292	2	no	—
76	Q₁₆	—	292	2	no	—
77	C₂×C₈	—	2	1	no	—
78	C₂×C₈	—	146	2	no	—
79	C₂×C₈	C₂²⋊D₇₃	1	1	yes	characteristic
80	C₂×C₈	C₂²⋊D₇₃	1	1	yes	characteristic
81	C₄⋊C₄	—	2	1	no	—
82	C₄⋊C₄	—	146	2	no	—
83	C₄⋊C₄	—	146	2	no	—
84	C₄⋊C₄	D₂₉₂	1	1	yes	characteristic
85	C₄²	—	2	1	no	—
86	C₄²	C₂²×D₇₃	1	1	yes	characteristic
87	Q₈	—	2	2	no	—
88	Q₈	—	292	2	no	—
89	Q₈	—	292	2	no	—
90	C₂×C₄	—	2	1	no	—
91	C₂×C₄	—	2	1	no	—
92	C₂×C₄	—	292	2	no	—
93	C₂×C₄	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
94	C₂×C₄	C₂×D₂₉₂	1	1	yes	characteristic
95	C₂×C₄	#11924028	1	1	yes	characteristic
96	C₈	—	2	1	no	—
97	C₈	—	4	1	no	—
98	C₈	—	292	2	no	—
99	C₈	#11924015	1	2	yes	—
100	C₂²	#14556565	1	1	yes	characteristic
101	C₄	—	2	1	no	—
102	C₄	—	4	1	no	—
103	C₄	—	4	1	no	—
104	C₄	—	584	2	no	—
105	C₄	C₂×#11924015	1	1	yes	characteristic
106	C₄	#14556616	1	1	yes	characteristic
107	C₄	#14556624	1	2	yes	—
108	C₂	#17988787	1	1	yes	characteristic
109	C₂	#17988845	1	1	yes	characteristic
110	C₂	#17988862	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#17988967

C₂

yes

maximal, characteristic

#17988872

C₂

yes

maximal

#17988338

C₂

yes

maximal, characteristic

#17988334

C₂

yes

maximal

#446×C₇₃

C₂

yes

maximal, characteristic

C₂×Dic₂₉₂

—

C₂×Dic₂₉₂

—

#14556591

C₂²

yes

—

#14556522

—

C₄⋊#10596831

C₂²

yes

—

#14556515

—

C₄×Q₈×C₇₃

C₂²

yes

characteristic

C₄⋊C₈×C₇₃

—

C₄⋊C₈×C₇₃

C₂²

yes

characteristic

#97×C₇₃

—

C₄×C₈×C₇₃

C₂²

yes

characteristic

C₂×Dic₁₄₆

—

Dic₂₉₂

—

Dic₂₉₂

—

C₂×#10596831

—

C₄⋊Dic₇₃

—

C₄⋊Dic₇₃

—

C₂×Q₈×C₇₃

D₄

yes

characteristic

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

D₄

yes

characteristic

C₂×C₈×C₇₃

D₄

yes

characteristic

C₄⋊C₄×C₇₃

—

C₄⋊C₄×C₇₃

D₄

yes

characteristic

C₄²×C₇₃

—

C₄²×C₇₃

C₂³

yes

characteristic

Q₈×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₂×D₄

yes

characteristic

C₂×C₄×C₇₃

C₂×D₄

yes

characteristic

C₂×C₄×C₇₃

#41

yes

characteristic

C₂×Dic₇₃

—

Dic₁₄₆

—

Dic₁₄₆

—

C₈×C₇₃

—

C₈×C₇₃

—

C₈×C₇₃

SD₁₆

yes

—

#10596831

—

C₂²×C₇₃

#121

yes

characteristic

C₄×C₇₃

—

C₄×C₇₃

—

C₄×C₇₃

—

C₄×C₇₃

C₂×SD₁₆

yes

C₄×C₇₃

yes

C₄×C₇₃

yes

—

Dic₇₃

—

C₂×C₇₃

yes

C₂×C₇₃

yes

C₂×C₇₃

yes

—

C₇₃

yes

characteristic, complemented, Sylow

#494

—

#475

—

#446

D₇₃

yes

characteristic

#334

—

#332

—

C₂×Q₁₆

—

146

—

C₂×Q₁₆

—

146

—

C₄⋊Q₈

—

C₄×Q₈

C₂×D₇₃

yes

characteristic

#106

—

146

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

C₂×D₇₃

yes

characteristic

#103

—

146

—

#97

—

C₄×C₈

C₂×D₇₃

yes

characteristic

C₂×Q₈

—

146

—

C₂×Q₈

D₂₉₂

yes

characteristic

Q₁₆

—

292

—

Q₁₆

—

292

—

C₂×C₈

—

C₂×C₈

—

146

—

C₂×C₈

C₂²⋊D₇₃

yes

characteristic

C₂×C₈

C₂²⋊D₇₃

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

146

—

C₄⋊C₄

—

146

—

C₄⋊C₄

D₂₉₂

yes

characteristic

C₄²

—

C₄²

C₂²×D₇₃

yes

characteristic

Q₈

—

Q₈

—

292

—

Q₈

—

292

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

292

—

C₂×C₄

C₂×C₂²⋊D₇₃

yes

characteristic

C₂×C₄

C₂×D₂₉₂

yes

characteristic

C₂×C₄

#11924028

yes

characteristic

C₈

—

C₈

—

C₈

—

292

—

C₈

#11924015

yes

—

100

C₂²

#14556565

yes

characteristic

101

C₄

—

102

C₄

—

103

C₄

—

104

C₄

—

584

—

105

C₄

C₂×#11924015

yes

characteristic

106

C₄

#14556616

yes

characteristic

107

C₄

#14556624

yes

—

108

C₂

#17988787

yes

characteristic

109

C₂

#17988845

yes

characteristic

110

C₂

#17988862

yes

characteristic

	subgroup	G/H
center	C₂²	#14556565
commutator	C₄²×C₇₃	C₂³
Frattini	C₄²	C₂²×D₇₃
Fitting	#446×C₇₃	C₂
socle	C₂²×C₇₃	#121
hypercenter	#446	D₇₃
hypocenter	C₇₃	#1690
LCS	G ▷ C₄²×C₇₃ ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #446

subgroup

G/H

center

C₂²

#14556565

commutator

C₄²×C₇₃

C₂³

Frattini

C₄²

C₂²×D₇₃

Fitting

#446×C₇₃

C₂

C₂²×C₇₃

D₇₃

C₇₃

G ▷ C₄²×C₇₃ ▷ C₂²×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #446

N	H ≅ G/N	type
56. C₇₃	#1690	semidirect

H ≅ G/N

type

56. C₇₃

#1690

semidirect

Subgroups — #22609425

Conjugacy classes of subgroups

Complements